What is the 6400th prime number?
The 6400th prime number is 63809. The next prime is 63823 (a gap of 14) and the one before is 63803.
Position
Pick any whole number from 1 to 10,000.
How to work it out
- 1
List the primes in order: 2, 3, 5, 7, 11, 13, ā¦ The 6400th one is 63809.
- 2
63809 is prime because no prime up to ā63809 ā 252.60 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 6400th prime is close to 6400 Ć ln(6400) ā 56090, and here it is 63809.
- 4
63809 has no twin: neither 63807 nor 63811 is prime.
Primes around the 6400th
| Position | Prime | Gap from the previous |
|---|---|---|
| 6397 | 63793 | 12 |
| 6398 | 63799 | 6 |
| 6399 | 63803 | 4 |
| 6400 | 63809 | 6 |
| 6401 | 63823 | 14 |
| 6402 | 63839 | 16 |
| 6403 | 63841 | 2 |
Questions
What is the 6400th prime number?
63809.
Which prime number is 63809?
63809 is the 6400th prime number.
What is the sum of the first 6400 primes?
193,100,475.